Question

The fuel cell just installed on campus converts energy from natural gas combustion into electrical work. Consider the combustion of methane, the primary component of natural gas:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

a. Predict the change in the extent of reaction as the temperature is increased at

constant total pressure.

b. Predict the change in the extent of reaction as the total pressure is increased at

constant temperature.

c. Calculate the maximum theoretical non-expansion work that can be extracted

from combustion of 1 mole of methane. Explain both the magnitude and the sign

of the work.

d. Calculate the maximum theoretical work that can be extracted from combustion

of 1 mole of methane in a heat engine. Assume Th = 900 K and Tc = 300 K.

e. How many moles of CO2 are produced per joule of work in an ideal fuel cell? An

ideal heat engine? Use your answers from (a) and (b).

f. In reality, most natural gas power plants have efficiencies around 40%, and most

fuel cells around 50%. How do those compare with the ideal efficiencies you

calculated? What are some possible reasons for the differences?

g. What other reasons might factor in to a choice between a natural gas power plant

and a natural gas fuel cell as a source of electricity?

Answer 1

B) Since you have 3 moles on the left and 1 mole on the right (gas moles) If you increase the pressure according to lechatelier principle the reaction will proceed in the direction where there are a small number of moles. Extent of reaction will increase

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

A) Enthalpy of methane : -74.8 KJ / mol

Oxygen = 0

CO2 = -393.5 KJ / mol

Water (liquid) = -285.5 KJ mol

According to the enthalpy definition

Entalphy = 2 *  -285.5 + (-393.5) - (2*0 + (-74.8)) = -890 KJ / mol

This reaction releases heat so this is an exothermic reaction, this will make that the reverse reaction occur, so we can say that the extent of reaction will decrease

C) Let´s calculate gibbs energy from tables (internet)

Methane = -50.72

Oxygen = 0

CO2 = -394.4

wate = -237 . 2

Gibbs = Products - Reactants = -394.4 + 2*(-237.2) - (-50.72 + 2*0) = -818 KJ / mol

The maximum non expansion work is -818 KJ / mol

W = Gibbs

D) maximum work of the combustion

-w = ( 1 - Tl/Th)*H_f

Th is the operating temperature

Tl is the temperature of the leaving gas, ill assume Tl = Tc

so

-w = (1-300/900)*-890 = -593.3 KJ/mol

w = 593.3 KJ / mol